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Mathematics > Algebraic Geometry
Title: Some Properties of Internal Locale Morphisms Externalised
(Submitted on 3 Jan 2023 (v1), last revised 24 Jul 2023 (this version, v2))
Abstract: We study morphisms of internal locales of Grothendieck toposes externally: treating internal locales and their morphisms as sheaves and natural transformations. We characterise those morphisms of internal locales that induce surjective geometric morphisms and geometric embeddings, demonstrating that both can be computed `pointwise'. We also show that the co-frame operations on the co-frame of internal sublocales can also be computed `pointwise' too.
Submission history
From: Joshua Wrigley [view email][v1] Tue, 3 Jan 2023 06:13:40 GMT (36kb)
[v2] Mon, 24 Jul 2023 16:15:23 GMT (43kb)
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